bloggin it up yeerd me :)
Linearization:
1.Identify the equation
2. Use the formula f(x)+f ' (x)dx
3. Determine your dx in the problem
4. Then determine your x in the problem
5. Plug in everything you get
6. Solve the equation
Related Rates:
1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation
tangent line
take the derivative of the equation and plug in the x-corrdinates to get your y,
then plug in y to get your slope then plug into the eqn.
MEAN VALUE THEOREM]
If f is continous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a number c in (a,b) such that F'(c) = f(b) - f(a) / b-a
IMPLICIT DERIVATIVE
while taking a derivative, anytime you take y', put a dy/dx in its place. then solve for dy/dx in terms of x.
i suck at integrals in a fraction. like substitution and all
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Usually integrals in a fraction are natural logs. If the top is the derivative of the bottom (the bottom being u), then the integral of it is ln |u| + c (if it's indefinite)
ReplyDeletemamie's right. it's usually a ln problem.
ReplyDeletego back in the notes & look for the stuff that bradni taught us that day right before she left.. when she just kinda went over everything and helped us out. she pointed out specific things to identify when your integrating fractions like if the top is the derivative of the bottom then it's ln integration. and how to identify whether or not it's tan inverse integration.
yeah, its usually natural logs, so the answer will pretty much always be the natural log of the bottom of the fraction, +c
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